Using TRACE

Quick start

1. Open TRACE and paste two columns from Excel into the Input box: NBRx (new patients) and TRx (total prescriptions), one row per month, starting at launch.
2. The fit runs as you type. Check the three fitted parameters and how closely the blue line follows the dots.
3. Set Months forward to project TRx, and choose how many new patients to assume each month.
4. Use Download Excel to take the results with you.

Click Load example to see a worked case on synthetic data.

Input format

Two columns, one row per period, oldest first. TRACE accepts pasted text, CSV, or Excel (.xlsx). The first sheet is used.

• Start at launch. Each month's TRx depends on every earlier cohort, so a series that starts mid-life leaves out patients who are already on therapy and the fit will be wrong.
• No gaps, oldest first, no negative values.
• At least 6 months are needed and 12 or more are recommended.
• Headers are optional. If present, NBRx and TRx are found by name in any case. Extra columns are ignored.
• Periods do not have to be months. If you use weeks, α comes out in weeks. The labels on the page say months.

Settings

Max lag

How many months of past cohorts count toward each month's TRx. The default is 36. A cohort older than the lag is treated as gone. Lowering it speeds up the calculation and limits the influence of very old patients. Raising it matters only when your series is longer than 36 months and a meaningful share of patients stay on therapy that long.

Months forward

How far to project TRx beyond your last month. Set it to 0 for a fit only.

Future new patients

A projection needs an assumption for new patients in the months to come.

• Average of last 3 months is the default.
• Hold last month repeats the most recent value.
• Custom per month uses a number you enter, for example from a brand forecast.

The projection is only as good as this assumption. TRACE does not forecast new patients.

Reading the results

In the retention table, Cum. dropout is 1 − S(t) and Monthly is the dropout in that month alone, S(t−1) − S(t).

A high R² does not prove the retention curve is right. Many combinations of α, β and k can fit a short series almost equally well. Compare the curve with anything you know about real persistence before relying on it.

Method

The Method page explains each equation, how the fit is found and what has been verified. In short: retention follows a Weibull survival curve. Total prescriptions come from adding up every past cohort that is still on therapy.

α, β and k are chosen to minimise the squared error between fitted and actual TRx. For any pair of α and β the best k has a closed form, so only α and β are searched, within 0.1 to 240 for α and 0.1 to 10 for β. TRACE tries several starting points to avoid a poor local minimum.

TRACE has been checked against an independent implementation of the same model. On our test datasets the two give the same α, β, k, RMSE and projections to at least five significant figures.

Limits

• It is an aggregate estimate. It does not follow individual patients. Patient-level claims with a Kaplan-Meier curve are more reliable when you have them.
• Short series are weakly identified. With under 12 months, α and β trade off against each other and the long tail is mostly extrapolation.
• Fill behaviour is folded into the curve. Refill gaps, late fills and compliance end up in S(t) and k, so the curve describes prescription-weighted persistence, not time on therapy.
• NBRx must really be new patients. If your source counts switches, restarts or all new prescriptions, the fit will mix groups that persist differently.
• All cohorts share one curve. Early adopters often persist differently from later patients.
• Data quality matters. Projected data, samples, free goods, copay-card or cash channels, and stocking can distort TRx, especially soon after launch.
• Projections depend on the new-patient assumption you choose.

Questions